Multilinear weighted estimates and quantum Zakharov system

Abstract

We consider the well-posedness theory of the compact case of one-dimensional quantum Zakharov system with the periodic boundary condition. The global well-posedness for sufficiently regular data is shown. The semi-classical limit as is obtained on a compact time interval whereas the quantum perturbation proves to be singular on an infinite time interval.

Keywords

• quantum Zakharov system
• well-posedness
• higher order perturbation